### Abstract

In this work the exact distribution of the linear combination of p independent logistic random variables is studied. It is shown that the exact distribution may be represented as a shifted infinite sum of independent random variables distributed as the difference of two independent Generalized Integer Gamma distributions. In addition, two near-exact approximations are developed for this distribution. Numerical studies are conducted to access the degree of precision and also the computational performance of these approximations. The developed methodology is used to derive near-exact approximations for the linear combination of independent generalized logistic random variables.

Original language | English |
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Pages (from-to) | 383-397 |

Number of pages | 15 |

Journal | Statistics, Optimization and Information Computing |

Volume | 6 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

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### Keywords

- Algebra of random variables
- Difference of Generalized Integer Gamma distributions
- Generalized Integer Gamma distribution
- Generalized logistic distributions
- Mixtures
- Shifted Gamma distribution